Assessment Pack — Mathematics 8

Term 1 · MATATAG Curriculum · Key Stage 3 · SY 2026–2027

⚠️ The weights are reported, and the Key Stage 3 attribution is an inference. See source-catalogue.md. The item content below is this repository's own work and stands on its own; confirm the weights before computing a real grade.

1. How assessment works this year

A single summative may not exceed half the item count of the term examination — 40 items, so 20 each. The Table of Specifications in §2 is this repository's, not DepEd's.

2. Table of Specifications — Term 1 Examination

40 items · Remembering · Understanding · Applying · Analysing

Factoring takes 22.5% for one week of teaching — the heaviest single-week weighting in any grade in this repository, and deliberately so. Week 8's rational expressions are factoring twice and cancelling; Grade 9's quadratics are factoring and then reading off roots. Nothing else in Grade 8 has that reach.

3. Summative Test 1 — Weeks 1–5

20 items · 40 minutes · end of Week 5

Part A · Measures of central tendency (items 1–6)

Use this data set for items 1–3: 4, 7, 7, 9, 13

1. Find the mean. ______
2. Find the median. ______
3. Find the mode. ______
4. Find the median of 2, 5, 5, 8, 10, 12. ______
5. A score of 20 is added to the set in items 1–3. What is the new mean? ______
6. Which measure of central tendency is most affected by one extreme value? ______

Part B · Monomials and the laws of exponents (items 7–13)

7. 3x² + 5x² = ______
8. 7ab − 2ab = ______
9. (2x³)(4x²) = ______
10. 12x⁵ ÷ 3x² = ______
11. (x³)⁴ = ______
12. (3x²)³ = ______
13. x⁵ · x⁰ = ______

Part C · Multiplying (items 14–20)

14. 2x(3x + 4) = ______
15. (x + 3)(x + 5) = ______
16. (x − 4)(x + 4) = ______
17. (x + 6)² = ______
18. (2x − 3)(x + 5) = ______
19. (x + 2)(x² + 3x + 1) = ______
20. (x − 5)² = ______

Answer key — Summative Test 1

Marking notes.

• Item 4 has an even number of values, so the median is the mean of the middle two: (5 + 8) ÷ 2 = 6.5. Learners who answer 5 or 8 have taken one middle value.
• Item 5 — the new total is 60 over 6 values. The mean rises from 8 to 10 on one score, which is the evidence for item 6 and worth pointing out after the paper.
• Item 12 — (3x²)³ = 27x⁶. The commonest error is 3x⁶, forgetting to cube the coefficient.
• Item 13 — x⁰ = 1, so the answer is x⁵. Learners who write x⁰ as 0 give 0; record it.
• Item 18 is the only product with a negative in the answer; item 19 the only one with three terms in a factor. Both are the discriminating items in Part C.

4. Summative Test 2 — Weeks 6–10

20 items · 40 minutes · end of Week 10

Part A · Special products (items 1–4)

1. (x + 7)(x − 7) = ______
2. (x + 5)² = ______
3. (3x − 2)² = ______
4. (2x + 5)(2x − 5) = ______

Part B · Factoring completely (items 5–13)

Factor each one completely.

5. x² − 25 = ______
6. 6x² + 9x = ______
7. x² + 7x + 10 = ______
8. x² − 9x + 20 = ______
9. x² + 12x + 36 = ______
10. 2x² − 50 = ______
11. x² − 3x − 10 = ______
12. 3x³ − 27x = ______
13. Can x² + 25 be factored? ______

Part C · Rational expressions (items 14–17)

14. Simplify (x² − 9) ÷ (x + 3). ______
15. Simplify 6x² ÷ 3x. ______
16. Simplify (x² + 5x + 6) ÷ (x + 2). ______
17. Solve x/3 = 4/6. ______

Part D · The Cartesian plane (items 18–20)

18. In which quadrant does (−3, 5) lie? ______
19. Find the distance between (0, 0) and (3, 4). ______
20. Find the midpoint of the segment joining (2, 4) and (6, 10). ______

Answer key — Summative Test 2

Marking notes.

• Items 10 and 12 each need two moves. Answers of 2(x² − 25) and 3x(x² − 9) are correct but incomplete — award half if you mark in halves, and record the names either way. This is the competency.
• Item 13 — accept "no" alone. A learner who adds "because it is a sum, not a difference" has met the harder half of Day 3.
• Items 14 and 16 are factoring in disguise: (x−3)(x+3)/(x+3) and (x+2)(x+3)/(x+2). A learner who cannot do them but factored Part B correctly has not yet connected the two — that is exactly what Week 8 is for.
• Item 9 — (x + 6)² and (x + 6)(x + 6) are the same answer. Accept both.

5. Term 1 Examination — Weeks 1–11

40 items · 60 minutes · end-of-term block

Part A · Measures of central tendency (items 1–5)

Use this set for items 1–3: 5, 8, 8, 11, 13, 15

1. Find the mean. ______
2. Find the median. ______
3. Find the mode. ______
4. One learner in a class of 20 scores 100; everyone else scores between 60 and 75. Which measure better describes the typical score — the mean or the median? Why? ______
5. Five numbers have a mean of 12. What is their total? ______

Part B · Expressions, monomials, exponents (items 6–11)

6. Write "five more than twice a number n" as an algebraic expression. ______
7. 4x² + 9x² = ______
8. (3x⁴)(5x³) = ______
9. 20x⁶ ÷ 4x² = ______
10. (x²)⁵ = ______
11. (2x³)⁴ = ______

Part C · Multiplying and special products (items 12–17)

12. 3x(2x − 5) = ______
13. (x + 4)(x + 6) = ______
14. (x − 8)(x + 8) = ______
15. (x + 9)² = ______
16. (3x + 2)(x − 4) = ______
17. (2x − 1)² = ______

Part D · Factoring completely (items 18–26)

Factor each one completely.

18. x² − 36 = ______
19. 7x² + 21x = ______
20. x² + 9x + 18 = ______
21. x² − 11x + 30 = ______
22. x² + 14x + 49 = ______
23. 4x² − 49 = ______
24. 3x² − 48 = ______
25. 2x³ − 8x = ______
26. A learner writes 5x² − 45 = 5(x² − 9). Is this correct? Is it completely factored? Finish it, and explain the difference between the two questions. ______

Part E · Problems with factors; simplifying (items 27–31)

27. A rectangle has area x² + 7x + 12. Give possible expressions for its length and width. ______
28. Simplify (x² − 16) ÷ (x − 4). ______
29. Simplify (x² + 8x + 15) ÷ (x + 5). ______
30. Simplify 8x³ ÷ 2x. ______
31. A square has area x² + 10x + 25. What is the length of one side? ______

Part F · Rational operations and sequences (items 32–36)

32. x/4 + x/4 = ______
33. (2/x) × (x/6) = ______
34. Solve x/5 = 6/10. ______
35. Write the next term: 3, 7, 11, 15, ______
36. State the rule for 2, 6, 18, 54, … and give the next term. ______

Part G · The Cartesian plane (items 37–40)

37. In which quadrant does (4, −2) lie? ______
38. Find the distance between (1, 2) and (4, 6). ______
39. Find the midpoint of the segment joining (−2, 3) and (6, 9). ______
40. A point lies on the x-axis and its x-coordinate is −5. Write its coordinates. ______

Answer key — Term 1 Examination

Marking notes — Term 1 Examination

• Item 26 is the highest-value item on the paper and the key Analysing item for Part D. Award in three steps: 1 for saying it is correct, 2 for saying it is not complete and finishing it, 3 for articulating the difference. A learner who only writes 5(x − 3)(x + 3) earns two marks, not three — the question asks for the distinction.
• Items 24 and 25 each need two moves. 3(x² − 16) and 2x(x² − 4) are correct and unfinished. Record which learners stop early; that is the week's diagnostic and it is what Week 8 will punish.
• Item 2 — six values, so the median is (8 + 11) ÷ 2 = 9.5. A whole-number answer is wrong.
• Item 11 — (2x³)⁴ = 16x¹². The commonest error is 2x¹², forgetting to raise the coefficient.
• Item 16 — 3x² − 10x − 8. Sign errors dominate here; the middle term is negative even though one binomial has a plus.
• Item 27 asks for possible dimensions, so (x + 4) and (x + 3) in either order is right. A learner who gives numbers has not read the question.
• Item 33 — (2/x)(x/6) = 2x/6x = ⅓. Accept 2/6 unsimplified with a note; accept 1/3.
• Item 36 carries two marks: one for the rule, one for 162.

Suggested mark allocation. One mark each for items 1, 2, 3, 5, 6–11, 12–17, 18–23, 28, 29, 30, 32, 33, 35, 37 and 40. Two marks each for items 4, 24, 25, 27, 31, 34, 36, 38 and 39. Three marks for item 26. That is 30 one-mark items, 9 two-mark items and one three-mark item — 51 marks over 40 items; scale to whatever your school records.

6. Week 7 weekly check

10 items · 15 minutes · Day 5 · Written Works Covers only competency Q1 · 8 — factor different types of polynomials completely.

Factor each one completely.

1. x² − 49 = ______
2. 4x² + 12x = ______
3. x² + 8x + 12 = ______
4. x² − 10x + 24 = ______
5. x² + 4x + 4 = ______
6. 2x² − 32 = ______
7. 3x³ − 12x = ______
8. Can x² + 16 be factored? ______
9. A learner writes 4(x² − 9). Is it completely factored? If not, finish it. ______
10. In one sentence: what does completely factored mean? ______

Answer key — Week 7 weekly check

Items 6, 7 and 9 are the whole check. A learner who gets 1–5 and 8 right and stops early on 6, 7 and 9 scores 7/10 while having missed the point of the week entirely — and that pattern is worth naming in the mark book rather than just totalling.

7. Performance task rubrics

All four use 4 criteria × 4 levels = 16 points. Convert with score ÷ 16 × 100.

7.1 The Tile Border — Term 1 task

7.2 Buying on Terms — Term 2 task

7.3 Two Plans, One Crossing — Term 3 task

7.4 Same Mean, Different Class — Term 3 task

7.5 Group activity rubrics

The two group activities in offline-activities.md carry their own 12-point rubrics. They are scored separately and also feed the Performance Tasks component.

8. What is deliberately not in this pack

Part of the E-turo MATATAG artifact set. Companion files: syllabus.md · lesson-plan.md · lesson-plan-ilaw.md · offline-activities.md · class-record.html · worksheet.html